The coronavirus crisis has exacerbated economic problems that worsened after U.S. President Donald Trump withdrew in 2018 from Iran's nuclear deal with major powers and reimposed sanctions. On Monday, Iran's rial currency fell to its lowest ever level against the US dollar.
"It's been the most difficult year due to the enemy's economic pressure and the pandemic," Rouhani said in a televised speech.
"The economic pressure that began in 2018 has increased ... and today it is the toughest pressure on our dear country."
Iran has seen a sharp increase in coronavirus infections and deaths since restrictions to stem the spread of the pandemic were gradually lifted from mid-April. The death toll has recently topped 100 a day for the first time in two months.
More than 220,000 cases have been confirmed, and over 10,000 deaths.
Rouhani said wearing of masks will become mandatory for two weeks starting next Sunday in "gathering places" that are deemed "red spots".
Senior officials have regularly warned that restrictions will be reimposed if health regulations such as social distancing to stem the surge in infections are not observed.Iran launched a campaign on Saturday to motivate a reluctant public to use face masks.